pdfgam {lmomco} | R Documentation

## Probability Density Function of the Gamma Distribution

### Description

This function computes the probability density function of the Gamma distribution given parameters (α, shape, and β, scale) of the distribution computed by `pargam`. The probability density function of the distribution has no explicit form, but is expressed as an integral.

f(x) = frac{1}{β^αΓ(α)} x^{α - 1} e^{-x/β} mbox{,}

where f(x) is the probability density for the quantile x. The parameters have the following interpretation in the R syntax; α is a shape parameter and β is a scale parameter.

### Usage

    pdfgam(x, para)

### Arguments

`x` | A real value.
`para` | The parameters from `pargam` or similar.

### Value

Probability density (f) for x.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`cdfgam`, `quagam`, `pargam`

### Examples

      lmr <- lmoms(c(123,34,4,654,37,78))
      gam <- pargam(lmr)
      x <- quagam(0.5,gam)
      pdfgam(x,gam)

[Package lmomco version 0.92 Index]